The director was appearing on U.K. TV show BBC Breakfast alongside actress Carey Mulligan to promote their film Drive.
Mulligan was seen cringing as the filmmaker described the level of violence in the action movie, insisting it was "a bit like f**king".
Horrified presenter Bill Turnbull quickly apologised for the remark and asked Winding Refn to "try and make the point without using that word".
Chiefs at the BBC have since issued viewers a further statement, which reads, "Unfortunately a guest used a swear word during a live interview. Bill Turnbull immediately challenged his language and both presenters apologised to viewers.
"There was a further apology at the end of the programme. We are sorry if anyone was offended."
The Oscar-winning actress appeared on the BBC Breakfast show, which airs between 6am and 9.15am local time, and let slip a four-letter word as she discussed her admiration for famed English thespian Sir John Gielgud.
Mirren paid tribute to the late actor and told of her love for his clipped accent, even when using curse words - before stunning presenters by uttering an obscenity.
She said, "He was always my inspiration for the choices he made, he was this great knight of the British theatre... that always inspired me. He always took such edgy choices, (and he would always say) in that wonderful voice he had, 'You little s**t'."
When the presenters pointed out her slip, Mirren clasped a hand over her mouth and laughed, adding, "Oops, I'm so sorry."
Presenter Bill Turnbull then told viewers, "That never happened. If you heard that, we are very sorry."